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A ClosedForm Solution for Mapping General Distributions to Minimal PH Distributions
 In Performance TOOLS
, 2003
"... Approximating general distributions by phasetype (PH) distributions is a popular technique in queueing analysis, since the Markovian property of PH distributions often allows analytical tractability. ..."
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Approximating general distributions by phasetype (PH) distributions is a popular technique in queueing analysis, since the Markovian property of PH distributions often allows analytical tractability.
Application of Network Calculus to General Topologies Using TurnProhibition
 IEEE/ACM Transactions on Networking
, 2002
"... Network calculus is known to apply in general only to feedforward routing networks, i.e., networks where routes do not create cycles of interdependent packet flows. In this paper, we address the problem of using network calculus in networks of arbitrary topology. For this purpose, we introduce a no ..."
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Cited by 24 (3 self)
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Network calculus is known to apply in general only to feedforward routing networks, i.e., networks where routes do not create cycles of interdependent packet flows. In this paper, we address the problem of using network calculus in networks of arbitrary topology. For this purpose, we introduce a novel graphtheoretic algorithm, called turnprohibition (TP), that breaks all the cycles in a network and, thus, prevents any interdependence between flows. We prove that the TPalgorithm prohibits the use of at most 1/3 of the total number turns in a network, for any network topology. Using analysis and simulation, we show that the TPalgorithm significantly outperforms other approaches for breaking cycles, such as the spanning tree and up/down routing algorithms, in terms of network utilization and delay bounds. Our simulation results also show that the network utilization achieved with the TPalgorithm is within a factor of two of the maximum theoretical network utilization, for networks of up to 50 nodes of degree four. Thus, in many practical cases, the restriction of network calculus to feedforward routing networks may not represent a too significant limitation.
A closed form solution for mapping general distributions to minimal ph distributions
 In International Conference on Performance Tools – TOOLS 2003
, 2003
"... Approximating general distributions by phasetype (PH) distributions is a popular technique in stochastic analysis, since the Markovian property of PH distributions often allows analytical tractability. This paper proposes an algorithm for mapping a general distribution, G, to a PH distribution, whi ..."
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Cited by 21 (1 self)
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Approximating general distributions by phasetype (PH) distributions is a popular technique in stochastic analysis, since the Markovian property of PH distributions often allows analytical tractability. This paper proposes an algorithm for mapping a general distribution, G, to a PH distribution, which matches the first three moments of G. Efficiency of our algorithm hinges on narrowing the search space to a particular subset of the PH distributions, which we refer to as EC distributions. The class of EC distributions has a small number of parameters, and we provide closedform solutions for these. Our solution applies to any distribution whose first three moments can be matched by a PH distribution. Also, our resulting EC distribution requires a nearly minimal number of phases, within one of the minimal number of phases required by any acyclic PH distribution. Key words: PH distribution, moment matching, closed form, normalized moment PACS: 1
Scheduling flows with unknown sizes: Approximate analysis
, 2002
"... Abstract Previous studies have shown that giving preferential treatment to short jobs helps reduce the average system response time, especially when the job size distribution possesses the heavytailed (HT) property. Since it has been shown that the TCP flow length distribution also has the same prop ..."
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Cited by 17 (1 self)
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Abstract Previous studies have shown that giving preferential treatment to short jobs helps reduce the average system response time, especially when the job size distribution possesses the heavytailed (HT) property. Since it has been shown that the TCP flow length distribution also has the same property, it is natural to let short TCP flows enjoy better service inside the network. Analyzing such discriminatory system requires modification to traditional job scheduling models since usually network traffic managers do not have detailed knowledge about individual flows such as their lengths. The MultiLevel queue, proposed by Kleinrock, can be used to to characterize such system. In this paper, we perform an approximate analysis on the MultiLevel queueing system to obtain closedform solution of the average system response time function. 1 Introduction Previous job scheduling studies indicate that providing rapid response to interactive jobs which place frequent but small demands, can reduce the overall system average response time [1]. Such sizeaware discriminatory scheduling algorithms have been shown, both experimentally and analytically (see [2] and references therein), to work extremely well when the job size distribution possesses the heavytailed (HT) property1. Since data transfer in a network can be modeled as a flow scheduling problem, and the HT property has been observed in the length of Internet transactions, especially Web file transfers, it is natural to design a network system that favors short file transfers.
Inference of link delay in communication networks
 IEEE J. Selected Areas in Communications
, 2006
"... Abstract—This paper studies the feasibility and algorithms for inferring the delay at each link in a communication network based on a large number of endtoend measurements. The restriction is that we are not allowed to measure directly on each link and can only observe the route delays. It is assu ..."
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Abstract—This paper studies the feasibility and algorithms for inferring the delay at each link in a communication network based on a large number of endtoend measurements. The restriction is that we are not allowed to measure directly on each link and can only observe the route delays. It is assumed that we have considerable flexibility in choosing which routes to measure. We investigate two different cases: 1) each link delay is a constant and 2) each link delay is modeled as a random variable from a family of distributions with unknown parameters. We will answer whether such indirect inference is possible at all, and when possible, how it can be carried out. The emphasis is on developing the maximumlikelihood estimators for scenario 2) when the link delays are modeled by exponential random variables or mixtures of exponentials. We have derived solutions based on the EM algorithm and demonstrated that, even though they do not necessarily reflect the true model parameters, they do seem to maximize the likelihood in most cases and that the resulting probability density functions match the true functions on regions where the probability mass concentrates. Index Terms—Expectation maximization (EM) algorithm, maximumlikelihood estimator, network delay measurement, network tomography.
Necessary and sufficient conditions for representing general distributions by Coxians
 In Proceedings of TOOLS '03
, 2002
"... A common analytical technique involves using a Coxian distribution to model a general distribution G, where the Coxian distribution agrees with G on the rst three moments. This technique is motivated by the analytical tractability of the Coxian distribution. Algorithms for mapping an input distribu ..."
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Cited by 9 (4 self)
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A common analytical technique involves using a Coxian distribution to model a general distribution G, where the Coxian distribution agrees with G on the rst three moments. This technique is motivated by the analytical tractability of the Coxian distribution. Algorithms for mapping an input distribution G to a Coxian distribution largely hinge on knowing a priori the necessary and sucient number of phases in the representative Coxian distribution. In this paper, we formally characterize the set of distributions G which are wellrepresented by an nphase Coxian distribution, in the sense that the Coxian distribution matches the rst three moments of G. We also discuss a few common, practical examples.
Analysis of multiserver systems via dimensionality reduction of Markov chains
 School of Computer Science, Carnegie Mellon University
, 2005
"... The performance analysis of multiserver systems is notoriously hard, especially when the system involves resource sharing or prioritization. We provide two new analytical tools for the performance analysis of multiserver systems: moment matching algorithms and dimensionality reduction of Markov chai ..."
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The performance analysis of multiserver systems is notoriously hard, especially when the system involves resource sharing or prioritization. We provide two new analytical tools for the performance analysis of multiserver systems: moment matching algorithms and dimensionality reduction of Markov chains (DR). Moment matching algorithms allow us to approximate a general distribution with a phase type (PH) distribution. Our moment matching algorithms improve upon existing ones with respect to the computational efficiency (we provide closed form solutions) as well as the quality and generality of the solution (the first three moments of almost any nonnegative distribution are matched). Approximating job size and interarrival time distributions by PH distributions enables modeling a multiserver system by a Markov chain, so that the performance of the system is given by analyzing the Markov chain. However, when the multiserver system involves resource sharing or prioritization, the Markov chain often has a multidimensionally infinite state space, which makes the analysis computationally hard. DR allows us to closely approximate a multidimensionally infinite Markov chain with a Markov
Performance of server selection algorithms for content replication networks
 In NETWORKING 2005
, 2005
"... Abstract. In this paper, we investigate the problem of optimal server selection in “content replication networks, ” such as peertopeer (P2P) and content delivery networks (CDNs). While a number of server selection policies have been proposed or implemented, understanding of the theoretical perform ..."
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Abstract. In this paper, we investigate the problem of optimal server selection in “content replication networks, ” such as peertopeer (P2P) and content delivery networks (CDNs). While a number of server selection policies have been proposed or implemented, understanding of the theoretical performance limits of server selection and the relative performance of existing policies remains limited. In this paper, we introduce a mathematical framework, based on the M/G/1 Processor Sharing queueing model, and derive closedform expressions for the optimal server access probabilities and the optimal average delay. We also analyze the performance of two general server selection policies, referred to as EQ DELAY and EQ LOAD, that characterize a wide range of existing algorithms. We prove that the average delay achieved by these policies can theoretically be as much as N times larger than the optimal delay, where N is the total number of servers in the system. Furthermore, simulation results obtained using our M/G/1PS workload model and the ProWGen Web workload generator show that the optimal policy can reduce the average delay of requests by as much as 30 % as compared to EQ LOAD and EQ DELAY, in realistic scenarios. They also show that the optimal policy compares favorably to the other policies in terms of fairness and sensitivity to traffic parameters. 1
unknown title
, 2003
"... A closedform solution for mapping general distributions to minimal PH distributions ..."
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A closedform solution for mapping general distributions to minimal PH distributions
A Comparative Analysis of Server Selection in Content Replication Networks
"... Abstract — Server selection plays an essential role in content replication networks, such as peertopeer (P2P) and content delivery networks (CDNs). In this paper, we perform an analytical investigation of the strengths and weaknesses of existing server selection policies, based initially on an M/G ..."
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Abstract — Server selection plays an essential role in content replication networks, such as peertopeer (P2P) and content delivery networks (CDNs). In this paper, we perform an analytical investigation of the strengths and weaknesses of existing server selection policies, based initially on an M/G/1 Processor Sharing (PS) queueingtheoretic model. We develop a theoretical benchmark to evaluate the performance of two general server selection policies, referred to as EQ DELAY and EQ LOAD, which characterize a wide range of existing server selection algorithms. We find that EQ LOAD achieves an average delay always higher than or equal to that of EQ DELAY. A key theoretical result of this paper is that in an Nserver system, the worstcase ratio between the average delay of EQ DELAY or EQ LOAD and the minimal average delay (obtained from the benchmark) is precisely N. We constructively show how this worstcase scenario can arise in highly heterogeneous systems. This result, when interpreted in the context of selfish routing, means that the price of anarchy in unbounded delay networks depends on the topology, and can potentially be very large. Our analytical findings are extended in asymptotic regimes to the G/G/1 FirstCome FirstServe and multiclass M/G/1PS models and supported by simulations run for various arrival and service processes, scheduling disciplines, and workload exhibiting temporal locality. These results indicate that our analysis is applicable to realistic scenarios. Index Terms — Content delivery networks, peertopeer networks, load balancing, distributed systems, price of anarchy, game theory. I.